Similar Figures:

Scale Factor

Ratio of Perimeters

Ratio of Areas

1. What is the scale factor for the similar parallelograms?

2. Solve for x in the pair of similar triangles.

8

15

16

30

30

25

12

x

3

5

6

10Scale Factor:

Ratio of the perimeters

= Scale Factor

6

3

Special Ratios in Similar Figures

10

5

2

1 2:1OR OR

2

1 2:1OR

Area Ratio

a b3

5

6

10

12 : 22 53a 106 b15a 60b

15 : 60

1 : 4

2:1

Scale Factor

Ratio of Areas

Simplify

Area Ratio Example

Given the Scale Factor is 3 : 5

Area Ratio is 32 : 52

9 : 25

The two rectangles are similar.

a. Find their scale factor. Use one pair of corresponding sides and simplify the ratio. The scale factor is 2 : 3.

b. Find the ratio of their perimeters. This is the same as the scale factor. or 2 : 3

c. Find the ratio of their areas. Square the scale factor. or 4 : 9

3

2

9

6

3

2

22 3:2

The similar figures above have a scale factor 3 : 4. The smaller figure has a perimeter of 15 inches. Find the perimeter of the larger figure.

Ratio of perimeters is the same as the scale factor. 3 : 4

Write a proportion.

Use cross products to solve. 3x = 60 x = 20 The larger figure has a perimeter of 20 inches.

x

15

4

3

The similar octagons above have a scale factor 2 : 5.

a. Find the ratio of their areas. Square the scale factor. 22 : 52 → 4 : 25

b. The larger figure has an area of 100 ft2. Find the area

of the smaller figure. Write a proportion. Use cross products to solve. 25x = 400 x = 16 The smaller octagon has an area of 16 ft2.

10025

4 x

Two similar paintings have perimeters of 20 in and 40 in.

a. Find the scale factor.

The scale factor is the same or 1 : 2 as the ratio of perimeters.

b. Find the ratio of the areas.

Square the scale factor. 12 : 22 → 1 : 4

2

1

40

20

Two similar paintings have perimeters of 20 in and 40 in.

The ratio of their areas is 1: 4.

c. The smaller area is 24 in2. Find the larger area.

Write a proportion using the ratio of the areas.

Use cross products to solve. x = 96

The larger area is 96 in2.

x

24

4

1

1. Use the similar hexagons below.

a) Find their scale factor.

b) Find the ratio of their perimeters.

c) Find the ratio of their areas.

2. Two similar triangles have perimeters of 12 m and 60 m

a) Find their scale factor.

b) Find the ratio of their areas.

12

18

Dylan has two similar trees in his backyard. One tree is twice as tall as the other. Suppose the trees were cut down in corresponding places. Each stump had a shape of a circle at its top. Is the area of the larger circle twice as big as the area of the smaller stump’s circle? Why or why not?

Special Ratios for Similar Figures

Lesson 10

If two figures are similar and the ratio of their sides simplifies to a :b, then:

The scale factor is a :b The ratio of the perimeters is a :b The ratio of the areas is a2:b2